Ballistic fingerprinting... From the Washington Times letters-to-the-editor, reader James Terpening raises at least one point that didn't occur to me:

Fourth, criminals would soon learn to swap the gun barrels of weapons they obtained, replace the original barrels with those manufactured illegally in clandestine factories, or change the ballistic fingerprint by scratching the inside of the barrel.

On semiautomatic handguns--as opposed to revolvers--it's child's play to swap barrels between guns of the same make.

Another good point is the sheer magnitude of the task compared to the minuscule data set you're seeking:

First, the expense of collecting, processing and storing such a database would be prohibitive, especially given its limited usefulness. A small fraction of firearms, about two-tenths of 1 percent, is ever used in the commission of a crime. There are more than 200 million firearms in the United States. Forcing American taxpayers or legitimate gun owners to pay for such a scheme is unfair. By Mr. Page's logic, in an effort to solve future crimes, we also could argue for fingerprinting and getting DNA samples from every baby born in the country.